Abstract
For S S a semitopological semigroup, a continuous function on S S is said to be in L M C ( S ) LMC(S) if its set of right translates is relatively compact in C ( S ) C(S) for the topology of pointwise convergence on S S . It is proved here that, if S S is a dense subsemigroup of a topological group G G , then every function in L M C ( S ) LMC(S) extends to a function continuous on G G . This result generalizes earlier results that were arrived at independently by A. T. Lau and the present author. Some corollaries of this result are also presented.
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